SCHRODINGER-MAXWELL SYSTEMS WITH INTERPLAY BETWEEN COEFFICIENTS AND DATA

this paper, we prove existence of a solution (u, phi) in W-0(1,2) (Omega) x W-0(1,2) (Omega) for the Schrodinger-Maxwell type system (*) { -div(M(x)del u) + a(x) phi vertical bar u vertical bar(r-2) u = f(x), in Omega, -div(N(x)del phi) = a(x) vertical bar u vertical bar(r), in Omega, u = phi = 0, on partial derivative Omega, with M and N bounded, uniformly elliptic matrices, r > 1, a(x) in L-1 (Omega) and f such that vertical bar f (x)vertical bar <= Q a(x) for some positive constant Q.